The Observed Growth of Massive Galaxy Clusters III: Testing General Relativity on Cosmological Scales

TL;DR

This work tests General Relativity on cosmological scales by jointly constraining the growth index $\gamma$ and the expansion history using a self-consistent analysis of massive galaxy clusters (238 X-ray–selected systems) and follow-up X-ray data. By parameterizing growth with $f(a)=\Omega_m(a)^{\gamma}$ and modeling non-linear structure through a calibrated $f(\sigma,z)$, the study combines cluster counts, gas fraction, SNIa, BAO and CMB to obtain tight gamma bounds. The results are consistent with GR and $\Lambda$CDM, with $\gamma(\sigma_8/0.8)^{6.8}=0.55^{+0.13}_{-0.10}$ and $0.79<\sigma_8<0.89$ under a flat $\Lambda$CDM background; relaxing scaling-evolution assumptions relaxes gamma constraints by only ~20%. The analysis demonstrates the robustness of GR on cosmological scales and underscores the importance of self-consistent treatment of cluster data and scaling relations for robust cosmological gravity tests.

Abstract

This is the third of a series of papers in which we derive simultaneous constraints on cosmological parameters and X-ray scaling relations using observations of the growth of massive, X-ray flux-selected galaxy clusters. Our data set consists of 238 clusters drawn from the ROSAT All-Sky Survey, and incorporates extensive follow-up observations using the Chandra X-ray Observatory. Here we present improved constraints on departures from General Relativity (GR) on cosmological scales, using the growth index, gamma, to parameterize the linear growth rate of cosmic structure. Using the method of Mantz et al. (2009a), we simultaneously and self-consistently model the growth of X-ray luminous clusters and their observable-mass scaling relations, accounting for survey biases, parameter degeneracies and systematic uncertainties. We combine the cluster growth data with gas mass fraction, SNIa, BAO and CMB data. This combination leads to a tight correlation between gamma and sigma_8. Consistency with GR requires gamma~0.55. Under the assumption of self-similar evolution and constant scatter in the scaling relations, and for a flat LCDM model, we measure gamma(sigma_8/0.8)^6.8=0.55+0.13-0.10, with 0.79<sigma_8<0.89. Relaxing the assumptions on the scaling relations by introducing two additional parameters to model possible evolution in the normalization and scatter of the luminosity-mass relation, we obtain consistent constraints on gamma that are only ~20% weaker than those above. Allowing the dark energy equation of state, w, to take any constant value, we simultaneously constrain the growth and expansion histories, and find no evidence for departures from either GR or LCDM. Our results represent the most robust consistency test of GR on cosmological scales to date. (Abridged)

Figures (5)

• Figure 1: 68.3 and 95.4 per cent confidence contours in the $\Omega_{\rm m},\gamma$ (left panel) and $\sigma_8, \gamma$ (right panel) planes for an assumed flat $\Lambda$CDM background model, using the combination of XLF, $f_{\rm gas}$, SNIa, BAO and CMB data. The gold, smaller contours assume self-similar evolution of the observable-mass scaling relations and constant scatter ($\beta_2^{\ell m}=0$; $\sigma_{\ell m}'=0$). The blue, larger contours allow for departures from self-similarity and redshift evolution in the scatter of the luminosity-mass relation (Section \ref{['sec:scal']}; Paper II). The horizontal, dashed lines mark $\gamma=0.55$, the growth index for GR.
• Figure 2: 68.3 and 95.4 per cent confidence contours in the $w,\gamma$ plane for the flat $w$CDM background expansion model, using the combination of XLF, $f_{\rm gas}$, SNIa, BAO and CMB data. The results assume self-similar evolution of the scaling relations and constant scatter ($\beta_2^{\ell m}=0$; $\sigma_{\ell m}'=0$). The horizontal, dashed line marks $\gamma=0.55$, the growth history for GR. The vertical, dotted-dashed line marks $w=-1$, the expansion history for $\Lambda$CDM. The results are simultaneously consistent with GR and $\Lambda$CDM.
• Figure 3: 68.3 and 95.4 per cent confidence contours in the $\beta^{\ell m}_2,\gamma$ (left panel) and $\sigma'_{\ell m}, \gamma$ (right panel) planes for the flat $\Lambda$CDM background evolution model, from the combination of XLF, $f_{\rm gas}$, SNIa, BAO and CMB data. The green, smaller contours show the constraints obtained with either $\beta^{\ell m}_2$ (left panel) or $\sigma'_{\ell m}$ (right panel) allowed to be a free parameter. The blue, larger contours show the results when both parameters, $\beta^{\ell m}_2$ and $\sigma'_{\ell m}$, are allowed to be free. The horizontal, dashed lines mark $\gamma=0.55$ (GR). The vertical, dotted-dashed lines mark the self-similar ($\beta^{\ell m}_2=0$; left panel) and constant scatter ($\sigma'_{\ell m}=0$; right panel) conditions.
• Figure 4: Marginalized constraints on $\gamma$ for the flat $\Lambda$CDM background expansion model, from the XLF data alone (green, dotted-dashed line), from the combination of SNIa, $f_{\rm gas}$, BAO and CMB data (red, dashed line), and from all the data sets combined, including the XLF (blue, solid line). It is clear that the XLF dominates the constraints on $\gamma$ and that, alone, it provides significantly tighter constraints than those from the combination of the other data sets.
• Figure 5: 68.3 and 95.4 per cent confidence contours in the $\Omega_{\rm m},\gamma$ (left panel) and $\sigma_8, \gamma$ (right panel) planes for the flat $\Lambda$CDM background expansion with self-similar evolution and constant scatter in the scaling relations. Results are shown for the following combinations of data sets: XLF+$f_{\rm gas}$ (red contours), XLF+$f_{\rm gas}$+SNIa (green contours), XLF+$f_{\rm gas}$+SNIa+BAO (blue contours), and XLF+$f_{\rm gas}$+SNIa+BAO+CMB (gold, smallest contours). This figure does not include the additional constraints on $\gamma$ from the ISW effect. The horizontal, dashed lines mark $\gamma=0.55$ (GR).